On the Eigenvalues of some Matrices based on Vertex Degree

Document Type : Research Paper


1 Department of Mathematics, Shahid Rajaee Teacher Training University

2 Department of mathematics, Shahid Rajaee Teacher Training University


The aim of this paper is to compute some bounds of forgotten index and then we present spectral properties of this index. In continuing, we define a new version of energy namely ISI energy corresponded to the ISI index and then we determine some bounds for it.


Main Subjects

1. K. C. Das and I. Gutman, Some properties of the second Zagreb index, MATCH
Commun. Math. Comput. Chem. 52 (2004) 103–112.
2. B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53 (2015)
3. B. Furtula, I.Gutman, Ž. KovijanićVukićević,G. Lekishvili and G. Popivoda, On an
oldd/new degree-based topological index, Bull. Acad. Serbe Sci. Arts (Cl. Sci.
Math. Natur.) 148 (2015) 19−31.
4. I. Gutman, An exceptional property of first Zagreb index, MATCH Commun. Math.
Comput. Chem. 72 (2014) 733−740.
5. I. Gutman, Edge decomposition of topological indices, Iranian J. Math. Chem. 6
(2015) 103−108.
6. I. Gutman, The energy of a graph, Ber. Math. Statist. Sekt. Forsch-ungszentram
Graz. 103 (1978) 1–22.
7. I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun.
Math. Comput. Chem. 50 (2004) 83–92.
8. I. Gutman and B. Furtula, Survey of graph energies, Math.Interdisc. Res. 2 (2017)
9. I. Gutman, B. Furtula, Ž. Kovijanić Vukićević and G. Popivoda, On Zagreb indices
and coindices, MATCH Commun. Math. Comput. Chem. 74 (2015) 5–16.
10. I. Gutman, Y. Hou, H. B. Walikar, H. S. Ramane and P. R. Hampiholi, No Hückel
graph is hyperenergetic, J. Serb. Chem. Soc. 65 (2000) 799–801.
11. A. Khaksari and M. Ghorbani, On the forgotten topological index, Iranian J. Math.
Chem. 8 (2017) 327−338.
12. I.Gutman and N.Trinajstić, Graph theory and molecular orbitals, Total π-electron
energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535−538.
13. X. Li and J. Zheng, A unified approach to the extremal trees for different indices,
MATCH Commun. Math. Comput. Chem. 54 (2005) 195−208.
14. S. Nikolić, G. Kovačević, A. Miličević and N. Trinajstić, The Zagreb indices 30
years after, Croat. Chem. Acta 76 (2003) 113–124.
15. G. Su, L. Xiong and L. Xu, The Nordhaus−Gaddum−type inequalities for the
Zagreb index and coindex of graphs, Appl. Math. Lett. 25 (2012) 1701–1707.
16. R. Todeschini and V. Consonni, Handbook of Molecular Descriptors,
Wiley−VCH, Weinheim, 2000.
17. D. Vukičević and M. Gašperov, Bond Additive Modeling 1. Adriatic Indices,
Croat. Chem. Acta 83 (2010) 243–260.
18. B. Zhou and N. Trinajstić, Some properties of the reformulated Zagreb index, J.
Math. Chem. 48 (2010) 714–719.